On Discontinuous Implicit Evolution Equations
Copyright policy )On Discontinuous Implicit Evolution Equations
Let \(J\) be an interval of the form \([0,T]\) of the real line. The paper deals with an IVP of the form \[ f(t,u(t), Lu(t))= 0,\tag{\(*\)} \] for a.e. \(t\in J\), \(u(0)= u_0\). Here, \(u\) is a function on \(J\) to an ordered \(B\)-space \(E\), \(L\) is a differential-like operator with values in \(L^p(J,E)\) and \(f\) satisfies some monotonicity conditions. The authors provide existence results for extremal solutions which are monotone nonincreasing w.r.t. \(f\) and monotone nondecreasing w.r.t. \(u_0\). Several applications and examples close the paper.
- Martin Luther University Halle-Wittenberg Germany
- University of Oulu Finland
- Oulu University Hospital Finland
Applied Mathematics, existence, implicit equations, Nonlinear differential equations in abstract spaces, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, monotonicity, Analysis, Implicit ordinary differential equations, differential-algebraic equations
Applied Mathematics, existence, implicit equations, Nonlinear differential equations in abstract spaces, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, monotonicity, Analysis, Implicit ordinary differential equations, differential-algebraic equations
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